Question

Using natural growth formula (FV=A(e^rt))

1)put $5K in a bank that pays interest at 3% annual rate, compounded continuously.What is the resulting amount after 12 years of interest assuming no money has been touched.

2) Current population is 300 million and rate growth of population is 4%. how many years until population increases by 50%?

2a)what will the population be in 25 years.

Answer 1

(1)

FV = PV x ert

FV ($) = 5000 x e(0.03 x 12) = 5000 x e(0.36) = 5000 x 1.4333 = 7166.5

(2)

(a)

Let number of years be N. Then

300 million x e(0.04 x N) = 1.50 x 300 million

e(0.04 x N) = 1.50

Taking natural log,

0.04 x N = 0.4055

N = 10.14 years

(b)

Population after 25 years (million) = 300 x e(0.04 x 25) = 300 x e(1.00) = 300 x 2.7183 = 815.49

NOTE: IN all cases, continuous compounding is assumed, as per formula given.